Unified Rating Equations for Cutthroat Flumes Derived from a Three-Dimensional Hydraulic Model

Computational fluid dynamics software was used to simulate the hydraulic behavior of 51 Cutthroat flume (CTF) sizes under various flow conditions, including 24 standard sizes with throat widths (W) from 0.051 to 1.219 m (2 inches to 4 ft), flume scale lengths (L) ranging from 0.457 to 2.743 m (1.5 - 9 ft), constriction ratios (W/L) of 1/9, 2/9, 3/9, and 4/9, and 27 non-standard flumes of intermediate sizes. The validity and accuracy of the simulation results were demonstrated using laboratory data from other studies for 16 of the standard flume sizes and three non-standard sizes. By using the depth-discharge data for 24 standard CTFs obtained from the modeling, a series of best-fit calibrations of existing separate free- and submerged-flow rating equations were performed for each of the 24 standard-sized CTFs. A new unified rating equation for free- and submerged-flow conditions for the standard CTF sizes was proposed by comparing a set of empirical equations. The performance of the unified rating equation was also analyzed in order to determine the technical desirability of the equations as substitutes for the existing separate free- and submerged-flow rating equations. For the free-flow rating, the discharge parameters in the traditional equation are generalized to be applicable to any of the CTF sizes with flume lengths ranging from 0.457 to 2.743 m (1.5 - 9 ft), and the constriction ratio ranging from 1/9 to 4/9. This allows the application of CTFs with greater accuracy than the previously available equation. With the new generic-fit equations for the free-flow rating parameters, the discharge error is 4% from the standard discharge, with an average error of 2.2% for full-scale discharge. The generic unified rating equations proposed herein are also applicable to any of the CTF sizes, varying among the 24 standard sizes with flume lengths ranging from 0.457 to 2.743 m (1.5 - 9 ft) and the constriction ratio ranging from 1/9 to 4/9. With the generic-fit equations for the calibration parameters as derived herein, the discharge error is 6 - 8% compared to the standard discharge, and 2 - 3% for full-scale discharge